Home
Class 12
MATHS
If (4+sqrt(15))^n=I+f,where n is an odd ...

If `(4+sqrt(15))^n=I+f,`where `n` is an odd natural number, `I` is an integer and ,then a.`I`is an odd integer b. `I`is an even integer c. `(I+f)(1-f)=1` d. `1-f=(4-sqrt(15))^n`

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP ENGLISH|Exercise All Questions|15 Videos

  • MATRICES

    RESONANCE DPP ENGLISH|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

If (2+sqrt(3))^n=I+f, where I and n are positive integers and 0lt f lt1 , show that I is an odd integer and (1-f)(1+f) =1

If (9 + 4 sqrt(5))^(n) = I + f , n and I being positive integers and f is a proper fraction, show that (I-1 ) f + f^(2) is an even integer.

(x+1) is a factor of x^n+1 only if (a)n is an odd integer (b) n is an even integer (c )n is a negative integer (d)n is a positive integer

(-i)^(4n+3) , where n Is a positive integer.

If (5 + 2 sqrt(6))^(n) = I + f , where I in N, n in N and 0 le f le 1, then I equals

If (sqrt(3)-i)^n=2^n, n in I , the set of integers, then n is a multiple of

If n is an odd integer, then (1 + i)^(6n) + (1-i)^(6n) is equal to

If sqrt(x) + sqrt(y)=4, f i n d (dx/dy) a t (y = 1).

If R = (7 + 4 sqrt(3))^(2n) = 1 + f , where I in N and 0 lt f lt 1 , then R (1 - f) equals

For a positive integer n , find the value of ( 1-i)^n(1-1/i)^ndot

RESONANCE DPP ENGLISH-JEE MAINS-All Questions
  1. Consider the points P(2,-4);Q(4,-2) and R(7,1). The points P,Q,R

    Text Solution

    |

  2. If plambda^4+qlambda^3+rlambda^2+slambda+t=lambda^2+3lambdalambda-1lam...

    Text Solution

    |

  3. If (4+sqrt(15))^n=I+f,where n is an odd natural number, I is an intege...

    Text Solution

    |

  4. If vec a= hat i+ hat j+ hat k and vec b= hat i-2 hat j+ hat k , then ...

    Text Solution

    |

  5. If lines (x-3)/1=(y-[K])/2=(z-1)/1 and (x-1)/2=(y+1)/3=(z-1)/4 interse...

    Text Solution

    |

  6. If S=1+4/3+9/9+(16)/(27)+oo, then find the value of [S] (where [.] is ...

    Text Solution

    |

  7. If A=[(a,b,c),(b,c,a),(c,a,b)],abc=1,A^(T)A=l, then find the value of ...

    Text Solution

    |

  8. Given four positive numbers in A.P. If 5, 6, 9 and 15 are added resp...

    Text Solution

    |

  9. Number of divisors of 2^5. 3^2 .5^3 which are divisible by 2 but not d...

    Text Solution

    |

  10. If alpha, beta are the roots of the quadratic equation x ^(2)+ px+q=0...

    Text Solution

    |

  11. f(x)=cos^(-1)(x-x^2)+sqrt(1-1/(|x|))+1/[[x^2-1]) then domain of f(x...

    Text Solution

    |

  12. The value of (lim)(nvecoo)sum(r=1)^(r-1)(sum(t=0)^(r-1)1/(5^n)dot^n Cr...

    Text Solution

    |

  13. If 25C0 25C2 +2. 25C1 25C3 +3. 25C2 .25C4+....+ 24. 25C23.25C25=k. 4...

    Text Solution

    |

  14. The graph of function f contains the point P(1, 2) and Q(s, r). The eq...

    Text Solution

    |

  15. Given that the 4th term in the expansion of [2+(3x//8)]^(10) has the m...

    Text Solution

    |

  16. Let A,B,C be 2xx2 matrices with entries from the set of real numbers. ...

    Text Solution

    |

  17. A person buys twelve packets of VANISH detergent. Each packet contai...

    Text Solution

    |

  18. Let f(n) denote the n^(th) terms of the seqence of 3,6,11,18,27,…. and...

    Text Solution

    |

  19. If the matrix A=[(0,2b,c) (a,b,-c) (a,-b,c)],A A^T=I then which of the...

    Text Solution

    |

  20. For |z-1|=1, i tan(("arg"(z-1))/(2))+(2)/(z) is equal to

    Text Solution

    |